Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 30Citation - Scopus: 31Heat and Mass Transport Impact on MHD Second-Grade Fluid: A Comparative Analysis of Fractional Operators(Wiley, 2021) Rehman, Aziz Ur; Riaz, Muhammad Bilal; Akgul, Ali; Saeed, Syed Tauseef; Baleanu, DumitruThe effect of the magnetic flux plays a major role in convective flow. The process of heat transfer is accompanied by a mass transfer process; for instance, condensation, evaporation, and chemical process. Due to the applications of the heat and mass transfer combined effects in different fields, the main aim of this paper is to do a comprehensive analysis of heat and mass transfer of magnetohydrodynamic (MHD) unsteady second-grade fluid in the presence of ramped conditions. The new governing equations of MHD second-grade fluid have been fractionalized by means of singular and nonsingular differentiable operators. To have an accurate physical significance of imposed conditions on the geometry of second-grade fluid, the constant concentration with ramped temperature and ramped velocity is considered. The fractional solutions of temperature, concentration, and velocity have been investigated by means of integral transform and inversion algorithm. The influence of physical parameters and flow is analyzed graphically via computational software (MATHCAD-15). The velocity profile decreases by increasing the Prandtl number. The existence of a Prandtl number may reflect the control of the thickness and enlargement of the thermal effect.Article Citation - WoS: 3Citation - Scopus: 2Surface Terms, Angular Momentum and Hamilton-Jacobi Formalism(Soc Italiana Fisica, 2003) Güler, Y; Baleanu, Dumitru; Baleanu, D; Cenk, M; MatematikQuadratic Lagrangians are introduced adding surface terms to a free-particle Lagrangian. Geodesic equations are used in the context of the Hamilton-Jacobi formulation of a constrained system. The manifold structure induced by the quadratic Lagrangian is investigated.Article Citation - WoS: 36Citation - Scopus: 41Numerical Treatment of Coupled Nonlinear Hyperbolic Klein-Gordon Equations(Editura Acad Romane, 2014) Doha, E. H.; Baleanu, Dumitru; Bhrawy, A. H.; Baleanu, D.; Abdelkawy, M. A.; MatematikA semi-analytical solution based on a Jacobi-Gauss-Lobatto collocation (J-GL-C) method is proposed and developed for the numerical solution of the spatial variable for two nonlinear coupled Klein-Gordon (KG) partial differential equations. The general Jacobi-Gauss-Lobatto points are used as collocation nodes in this approach. The main characteristic behind the J-GL-C approach is that it reduces such problems to solve a system of ordinary differential equations (SODEs) in time. This system is solved by diagonally-implicit Runge-Kutta-Nystrom scheme. Numerical results show that the proposed algorithm is efficient, accurate, and compare favorably with the analytical solutions.Article Citation - Scopus: 4On Mild Solution of Abstract Neutral Fractional Order Impulsive Differential Equations With Infinite Delay(Eudoxus Press, LLC, 2018) Anguraj, A.; Baleanu, Dumitru; Kanjanadevi, S.; Baleanu, D.; MatematikWe prove the existence and uniqueness of fractional neutral impulsive differential equations with infinite delay via contraction mapping principle and fixed point technique for condensing map. We use the resolvent operator technique for integral equations to make the mild solution of the problem more appropriate. © 2018 by Eudoxus Press, LLC. All rights reserved.Article Modelling the Latex Spreading on Clay(Chiminform Data S A, 2014) Al-Turaif, Hamad A.; Baleanu, Dumitru; Baleanu, Dumitru; MatematikIn this manuscript a model was proposed in order to predict the extent of the latex spreading on clay pigment. The results from Scan Electron Microscopy (SEM) and X-ray Photoelectron Spectroscopy (XPS) were used to evaluate the predicted results. A good agreement of the predicted results was found.Article Citation - WoS: 8Citation - Scopus: 8Determination of Salicin Content of Some Salix L. Species by Hplc Method(Chiminform Data S A, 2007) Guvenc, Aysegul; Baleanu, Dumitru; Arihan, Okan; Altun, M. Levent; Dinc, Erdal; Baleanu, Dumitru; MatematikIn this paper, we find the salicin content of the nine species of Salix L from the province of Ankara, Turkey, namely Salix triandra, S. alba, S. excelsa, S. fragilis, S. babylonica, S. caprea, S. cinerea, S. pseudomedemii and S. amplexicaulis. A simple HPLC method was applied to the determination of Salicin of these nine species in barks and leaves of female and male. Chromatographic separation was carried out by a mobile phase consisting of bidistilled water, tetrahydrofuran and ortho-phosphoric acid (97.7: 1.8: 0.5) (v/v/v). The salicin amount of these samples was analyzed by measuring the peak area at the wavelength, 270 nm. A reversed phase phenyl column (250 x 4.6mm, 5 mu m) was used and flow rate was set to 1 ml/min. in an isocratic elution. The results provided 6 HPLC method was found in agreement with those indicated by European Pharmacopoeia. It was observed that S. babylonica female bark sample possess the highest salicin content (2.675), while S. caprea female bark (0.058) has the lowest salicin content as w/w (%).Article Citation - WoS: 4Citation - Scopus: 4Fractional Vector Calculus in the Frame of a Generalized Caputo Fractional Derivative(Univ Politehnica Bucharest, Sci Bull, 2018) Jarad, Fahd; Gambo, Yusuf Ya'u; Baleanu, Dumitru; Jarad, Fahd; Baleanu, Dumitru; Abdeljawad, Thabet; Abdeljawad, Thabet; MatematikThe authors in [1] recently introduced a new generalized fractional derivative on AC(y)(n)[a ,b] and C-y(n)[a, b], and defined their Caputo version. This derivative contains two parameters and reduces to the classical Caputo derivatives if one of these parameters tend to certain values. From here and after, by generalized Caputo fractional derivative, we refer to the Caputo version of the generalized fractional derivative. This paper studies the generalized Caputo fractional derivative and establishes the Fundamental Theorem of Fractional Calculus (FTFC) in the sense of this derivative. The fundamental results are used in establishing some vital theorems and then applied to vector calculus.Article Citation - WoS: 5Citation - Scopus: 5Performance Evaluation of Matched Asymptotic Expansions for Fractional Differential Equations With Multi-Order(Soc Matematice Romania, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Sayevand, Khosro; MatematikAn extension of the concept of the asymptotic expansions method is presented in this paper. The multi-order differential equations of fractional order are investigated and the convergence of the proposed method is proven. The reported results show that the present approach is very effective and accurate and also are in good agreement with the ones in the literature.Article Citation - WoS: 4Citation - Scopus: 32d Gravity and the Hamilton-Jacobi Formalism(Soc Italiana Fisica, 2002) Baleanu, D; Baleanu, Dumitru; Güler, Y; MatematikHamilton-Jacobi formalism is used to study 2D gravity and its SL(2, R) hidden symmetry. If the contribution of the surface term is considered, the obtained results coincide with those given by the Dirac and Faddeev-Jackiw approaches.Article Citation - WoS: 16Citation - Scopus: 16Comparative Application of Wavelet Approaches To Absorption and Ratio Spectra for the Simultaneous Determination of Diminazene Aceturate and Phenazone in Veterinary Granules for Injection(Govi-verlag Pharmazeutischer verlag Gmbh, 2005) Dinç, E; Baleanu, Dumitru; Kanbur, M; Baleanu, D; MatematikA comparison of two wavelet approaches, Daubechies and reverse Biorthogonal, is described for the quantitative resolution of a binary mixture of diminazene aceturate (DIMA) and phenazone (PHE) in veterinary granules for injection without any chemical separation. These two approaches were specified as db4 (a = 180) and rbior3.7 (a = 125) respectively, after testing the signal analysis parameters for the overlapping absorption spectra and ratio spectra. In the first step db4 (a = 180) was applied to the original absorbance data vector of DIMA and PHE. In the second step rbio3.7 (a = 125) was applied to the ratio spectra data vectors of DIMA using the divisor PHE. The same approach was also subjected to the ratio spectra of PHE using the divisor DIMA. The db4 (a = 180) and rbior3.7 (a = 125) calibration graphs were constructed using the transformation values obtained in the wavelet domain. In the method validation, the wavelet calibration functions were tested using synthetic mixtures and the standard addition technique. The simultaneous quantitative analysis of DIMA and PHE in the commercial veterinary preparation was achieved by the elaborated methods. The assay results were compared with each other and good agreement was observed.